The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{-4}$ is $\dots \; kJ / m ^{3}$. Assume that material is elastic upto the linear strain of $5 \times 10^{-4}$.
JEE MAIN 2022, Medium
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$y =\frac{\text { stress }}{\text { strain }}=2.0 \times 10^{10}$
Energy density $=\frac{1}{2} \; stress \; \times \; strain$
$=\frac{1}{2}(\text { strain })^{2} y =\frac{1}{2}\left(5 \times 10^{-4}\right)^{2} \times 20 \times 10^{10}$
$=25 \times 10^{2} \times 10=25 \frac{ kJ }{ m ^{3}}$
Ans. $25$
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